Engineering task and calculation objective
This module calculates the heat transfer in film boiling per Chapter H2.6 of the VDI Heat Atlas (VDI-Wärmeatlas, 12th German edition, 2019). In film boiling, a closed vapor film separates the heated wall from the liquid: heat must be transferred through conduction and convection in the vapor film, plus additionally through radiation. The heat transfer coefficient is one to two orders of magnitude smaller than in nucleate boiling, and the wall temperatures are correspondingly high.
This calculation is needed whenever heated surfaces are operated above the Leidenfrost temperature or when operation beyond the critical heat flux must be assessed: when estimating wall temperatures after a boiling crisis, when quenching hot components (hardening), for immersed tubes in molten metals and salts, or for cryogenic fluids, which on warm walls practically always exhibit film boiling. Engineers who want to calculate film boiling need the vapor property data at the mean film temperature and the wall temperature.
The module superimposes the conduction/convection contribution in the vapor film with the radiation contribution derived from the radiation exchange constant, and delivers the resulting heat transfer coefficient and the heat flux for the characteristic geometry (tube or plate).
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation workflow
- Define the temperatures: From the wall temperature ϑ_w and the boiling temperature ϑ_s, the driving temperature difference ϑ_w − ϑ_s and the mean vapor film temperature (ϑ_w + ϑ_s)/2 are formed; the vapor properties are evaluated at the latter.
- Determine the vapor film properties: Density, specific heat capacity, thermal conductivity, and dynamic viscosity of the vapor are taken at the mean film temperature; in addition, the liquid density, the density difference ρ' − ρ_g, and the enthalpy difference extended by the vapor superheat enter the calculation.
- Calculate the conduction contribution in the vapor film: Using the characteristic length (tube: diameter, plate: height) and the gravitational acceleration, the heat transfer coefficient of the laminar vapor film flow is determined — analogous to Nusselt film theory, but with the vapor film as the heat-conducting layer.
- Superimpose the radiation contribution: The radiation heat transfer coefficient follows from the radiation exchange constant and the temperatures of wall and liquid. Since radiation thickens the film, it is not simply added but superimposed on the conduction contribution with a weighting factor.
- Evaluate the result: The resulting heat transfer coefficient and the heat flux q̇ = α·(ϑ_w − ϑ_s) describe the operating point on the film boiling branch of the boiling curve.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Boiling pressure | ps | Pa |
| Boiling temperature | ϑs | °C |
| Density | ρ' | kg/m³ |
| Density | ρ'' | kg/m³ |
| Specific heat capacity | cp'' | J/(kg·K) |
| Thermal conductivity | λ'' | W/(m·K) |
| Dynamic viscosity | η'' | mPa·s |
| Heat of evaporation | Δhv | J/kg |
| Characteristic length (Tube: Diameter, Plate: Height) | L | m |
| Wall temperature | ϑw | °C |
| Acceleration due to gravity | g | m/s² |
| Radiation transfer coefficient | C12 | W/m²/K^4 |
| Factor | Kf (31) | – |
| Temperature difference (ϑw - ϑs) | Δϑ | K (diff) |
| Mean gas temperature (ϑw+ϑs)/2 | ϑg | °C |
| Mean gas density | ρg | kg/m³ |
| Density difference (ρ'- ρg) | Δρ | kg/m³ |
| Enthalpy difference | Δhg | J/kg |
| Heat transfer coefficient radiation | αs | W/(m²·K) |
| Heat transfer coefficient conduction | αL | W/(m²·K) |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Heat transfer coefficient | αF (30) | W/(m²·K) |
| Heat flux | q̇F | W/m² |
Frequently asked questions
From what point on does film boiling occur?
Stable film boiling establishes itself above the Leidenfrost temperature, i.e. at wall superheats at which the liquid can no longer wet the wall. Between the critical heat flux and the Leidenfrost point lies the unstable transition boiling regime, which is not captured by steady-state calculation. With an imposed heat flux, the system jumps from the boiling crisis directly onto the film boiling branch.
Why are the vapor properties evaluated at the mean film temperature?
In the vapor film, the temperature drops from the hot wall to the boiling temperature; the property data change considerably across the film thickness. Evaluation at the arithmetic mean (ϑ_w + ϑ_s)/2 is the documented approximation with which the correlation is calibrated — using properties at the boiling temperature underestimates the film temperature and distorts the result.
When must the radiation contribution be considered?
The conduction contribution in the vapor film is small, so radiation becomes noticeable from wall temperatures of just a few hundred degrees Celsius and dominates on glowing surfaces (quenching, fire exposure). Since the radiative heat flux increases the evaporation rate and thus the film thickness, it must not simply be added; the module's superposition formula weights it accordingly.